a)
[tex]2x-(x+3)=6+2x\\\\-x-3=6\\\\-x=6+3\\\\-x=9\\\\\boxed{x=-9}[/tex]
b)
[tex]\frac{1}{2}(x+5)=\frac{2}{3}x+1~~~~~~~~|~*2\\\\x+5=\frac{4}{3}x+2~~~~~~~~|~*3\\\\3x+15=4x+6\\\\3x-4=6-15\\\\-x=-9\\\\\boxed{x=9}[/tex]
c)
[tex]\frac{x+1}{2}-\frac{x}{5}=\frac{5x+2}{10}~~~~~~~~|~*10\\\\5(x+1)-2x=5x+2\\\\5x+5-2x=5x+2\\\\5-2x=2\\\\-2x=2-5\\\\-2x=-3\\\\\boxed{x=\frac{3}{2}}[/tex]
d)
[tex]x(1+x)-1=-x^{2}+2(3x+x^{2})\\\\x+x^{2}-1=-x^{2}+6x+2x^{2}\\\\x+x^{2}-1=x^{2}+6x\\\\x-1=6x\\\\x-6x=1\\\\-5x=1\\\\\boxed{x=-\frac{1}{5}}[/tex]
